LEG 5 - BWI - EWR (still looking for two airlines, each operating a different type of turboprop aircraft); BWI - LGA, AL, DH7 (still looking for one additional airline operating a turboprop)
I will throw in the towel on this last one if there are no more speculations by tomorrow (Thurs) evening
BONUS PERMUTATION QUESTION:
if you end Leg 3 in a different metropolitan area, and therefore fly a different Leg 4 and Leg 5, you will replace two jet types with one jet and one turboprop, and still satisfy the multiple-models and no repeat airlines criteria
LEG 3A -- LAX to XXX Metro Area (jet)
LEG 4A -- XXX Metro Area to YYY Metro Area (turboprop)
LEG 5A -- YYY Metro Area to NYC Metro Area (turboprop)